Answer: The slope is -0.7, the rise is -1.4, and the run is 2
Jasmine, multiply your age by 3 and add 6. Thenmultiply this sum by 2. James, multiply your age by 2and add 4. Then multiply this sum by 3. I predict youwill both get the same number!») B. Choose 4 whole numbers for the twins' age and test eachexpression. Make a table to show the numbers you tried and theresults.
Same age
See explanation below
Explanation:Let the age of Jasmine = y
Multiplying Jasmine age by 3 and adding 6:
= (y × 3) + 6
= 3y + 6
Multiplyng the sum by 2:
2 × the sum = 2 × (3y + 6)
= 6y + 12
Let James age = z
Multiplying the age by 2 and adding 4:
James age × 2 = z × 2 = 2z
adding 4 = 2z + 4
Multiplying the sum y 3:
3 × the sum = 3 × (2z + 4)
= 6z + 12
Now since they are twins, they ae most likely same age
This means:
6y + 12 = 6z + 12
subtracting 12 from both sides:
6y = 6z
dividing both sides by 6:
y = z
Hence, Jasmine age is the same as James age
B) The expression for Jasmine = 2(3y + 6) = 6y + 12
The expression for James = 3(2z + 4) = 6z + 12
let the twin's age = 2, 3, 4, 5
when twin's age = 2
6y + 12 = 6(2) + 12 = 12 + 12 = 24
6z + 12 = 6(2) + 12 = 12 + 12 = 24
when twin's age = 3
6y + 12 = 6(3) + 12 = 18 + 12 = 30
6z + 12 = 6(3) + 12 = 18 + 12 = 30
when twin's age = 4
6y + 12 = 6(4) + 12 = 24 + 12 = 36
6z + 12 = 6(4) + 12 = 24 + 12 = 36
when twin's age = 5
6y + 12 = 6(5) + 12 = 30 + 12 = 42
6z + 12 = 6(5) + 12 = 30 + 12 = 42
Plotting the table:
Have no clue how to do this if you could help or give best guess that would be awesome.
We are asked to find an equivalent amount to 100 USD in french francs. Acording to the table, on tuesday, a dollar costs 4.3450 french francs, then we can find how many francs we got by multiplying 100 USD and 4.345, then we get:
Francs = 100×4.3450 = 434.50
Then, the answer is 434.5 french francs
A travel trailer is bought at the price of $35,000. The value decreases at the rate of .25 every year (t). The exponential expression 35,000(0.75)t describes this situation. Find the value of the travel trailer after 5 years.
The value of the travel trailer after 5 years is $8306 .
in the question ,
it is given that
the price of the travel trailer(a) = $35000
rate of decrease(r) = 0.25
time (x) = 5 years
The exponential expression for the decrease in price after x years is given by the formula
price = a(1-r)ˣ
where, a is the initial amount ,
r is the decay rate ,
x is the time period .
Substituting the values from above in the formula ,
we get
price = 35000(1-0.25)⁵
= 35000(0.75)⁵
= 8305.664
≈8306
Therefore , the value of the travel trailer after 5 years is $8306 .
Learn more about Exponential Expression here
https://brainly.com/question/13958067
#SPJ1
Select the diagram that shows the segment AC:
THE ANSWER IS IN THE PICTURE BELOW
Answer:
Its A
Step-by-step explanation:
that's literally what a segment is
5. For which values of x and y is line p parallel to line q? (1 point)
R
(26y)⁰
Ox= 5, y = 3
Ox= 1, y = 5
Ox=3, y=5
Ox=3, y=6
(16x + 2)°
(45x-51
Answer:
x = 3 and y = 5
Step-by-step explanation:
1st: The sum of the same side interior angles equal 180°. Use this to solve for x.
45x - 5 + 16x + 2 = 180
61x - 3 = 180
61x - 3 + 3 = 180 + 3
61x/61 = 183/61
x = 3
2nd: find the measure of angle 16x + 2
16x + 2
16(3) + 2
48 + 2
50°
3rd: the sum of the 50° angle and the angle 26y° is 180 since they make a straight angle. Make an equation and solve for y.
50 + 26y = 180
50 - 50 + 26y = 180 - 50
26y = 130
26y/26 =130/26
y = 5
2q/5 + 4 < 2q/ - 9 what the solution set?
The solution set for the given inequality (2q/5 + 4 < 2q/-9) is q∈(-∞, - 45/7).
What is the solution set?A solution set is a group of values in mathematics that satisfy a given set of equations or inequalities.Any value of a variable that causes the given equation to hold true is a solution. A solution set is a collection of all the variables needed to solve an equation. Due to the fact that 2y + 6 = 14 and 2(4) + 6 = 14, the solution set is 4. You must first enter each value from the domain into the equation to obtain the corresponding range values before you can determine the solution set of an equation with a given domain.From these values, make ordered pairs, and then write them as a set.So, 2q/5 + 4 < 2q/ - 9:
Now, solve for the solution set as follows:
2 ∙ q/5 + 4 < 2 ∙ q/ - 92 ∙ q/5 + 4 < - 2 ∙ q/92q/5 + 4 < - 2q/9[(2q) + 5∙4]/5 < - 2q/9q ∈ ( -∞, - 45/7)Therefore, the solution set for the given inequality is q ∈ ( -∞, - 45/7).
Know more about the solution set here:
https://brainly.com/question/10588366
#SPJ13
if a 95% confidence interval for the mean head circumference for adults, based on the results of measuring head circumference for 30 adults, is (21.42, 23.18) inches, what is the margin of error? inches.
The margin of error is 0.88.
What is a margin of error?
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings.
Here, we have
Lower confidence interval = 21.42
Upper confidence interval = 23.18
Now,
Sample mean(x) = (Lower confidence interval + Upper confidence interval)/2
x = (21.42 + 23.18)/2
x = 44.6/2
Sample mean (x) = 22.3
Now, we find the margin of error,
margin of error = Upper confidence interval - x
= 23.18 - 22.3
= 0.88
Hence, the margin of error is 0.88.
To learn more about the margin of error from the given link
https://brainly.com/question/28964736
#SPJ4
The margin of error is 0.88.
What is a margin of error?In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings.Here, we have
Lower confidence interval = 21.42Upper confidence interval = 23.18Now, calculate:
Sample mean(x) = (Lower confidence interval + Upper confidence interval)/2
x = (21.42 + 23.18)/2x = 44.6/2Sample mean (x) = 22.3Now, we find the margin of error:
margin of error = Upper confidence interval - x
= 23.18 - 22.3= 0.88Hence, the margin of error is 0.88.
To learn more about the margin of error from the given link
https://brainly.com/question/10218601
#SPJ4
Question 19:
1 2 2 4 8 32 ?
Answer:
256
Step-by-step explanation:
1,2,2,4,8,32
1*2=2
2*2=4
4*2=8
8*4=32
632*8=256
7. The vertices of a triangle are P(-7,-4), Q(-7, -8), and R(3, -3). Name the vertices of the
image reflected across the line y=x.
OP(4, 7), Q8, 7), R'(3,-3)
OP(4,-7), Q8, -7), R'(3, 3)
OP(-4,-7), Q(-8,-7), R'(-3, 3)
OP(-4, 7), Q(-8, 7), R'(-3,-3)
(1 point)
A place where two or more curves, lines, or edges converge is known as a vertex in geometry (plural: vertices or vertexes), and it is frequently identified by letters like,,,. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.
The solutions are:
P' = (-4,-7)
Q ' = (-8,-7) (-8,-7)
R ' = (-3,3) (-3,3)
All you have to do is flip the provided points P, Q, and R's x and y coordinates.
The common principle is (x,y) —-> (y,x)
Thus, when we reflect across the line y = x, something like P = (-7,-4) becomes P'= (-4,-7). The similar approach is taken with the other points.
How do you locate a triangle's vertices?
Finding the triangle's vertices on the line y = x as an image
The steps below are used to locate a triangle's vertices using its midpoints:
Identify the midpoints' x and y values;
Calculate the midpoint using the following equations: A = (x 1+ x 3 - x 2, y 1 + y 3-y 2); B = (x 1+x 2-x 3, y 1+y 2-y3); C = (x 2+x 3-x 1, y 2 + y 3 -y 1);.
To learn more about Triangle vertices refer to:
https://brainly.com/question/28061731
#SPJ13
Which answer seems the most reasonable answer to the problem below? *
(-5.6) (3.4) =
-20
18
-15
12
Answer:
-20
Step-by-step explanation:
1- each of the two numbers are inside parenthesis and are beside each other which means they should be multiplied like this: -5.6 * 3.4
2- because 5.6 is negative, the rule in multiplying different signs would result to a negative number
3- and when you accurately multiply them, the answer is 19.04, and the options here are estimated so you should estimate the 19.04 too
4- 1 after it is 9 and nine is a great number, 1 turns to 2 and 9 turns into 0, which equals to 20, and DO NOT forget to add the sign, which is negative as i said previously
how many lines of symmetry does the word checkbook have?
Answer:
none (as shown) or
one if all uppercase letters
Step-by-step explanation:
A line of symmetry is a line you could place on a shape (usually a square, rectangle, triangle, etc, but here the "shape" is the word checkbook) which, if you folded the shape on the line, the two halves of the shape would exactly match each other.
"checkbook" does NOT have any lines of symmetry. BUT,
CHECKBOOK
does have a line of symmetry, horizontally, right thru the middle.
When solving the system of equations below, which expression could be substituted for x in the second equation? x=4−y
3x+2y=15
The expression that we can replace in the second equation is 4 - y, doing that, we will get the solutions:
x = -8 and y = 12
How to solve the solve the system by substitution?
Here we have the system of equations:
x=4−y
3x+2y=15
Notice that x is already isolated on the first equation, so we can substitute that in the second equation. Then we will get:
3x+2y=15
3*(4 - y) + 2y = 0
So the expression that could be substituted for x in the second equation is 4 - y.
And now we get:
12 - 3y + 2y = 0
12 = y
And the value of x is:
x = 4 - y = 4 - 12 = -8
Learn more about systems of equations.
https://brainly.com/question/13729904
#SPJ1
if the work required to stretch a spring 3 ft beyond its natural length is 15 ft-lb, how much work (in ft-lb) is needed to stretch it 18 in. beyond its natural length? give your answer in decimal form.
The amount of work needed to stretch the spring 18 in. from its natural position is 3.75 ft-lb.
According to the Hooke's Law, the work done on the spring is:
W = 1/2. k . x²
Where:
k = spring constant
x = displacement.
Notice that the work done is directly proportional to x².
Hence,
W₁ : W₂ = x₁² : x₂²
Parameters given:
W₁ = 15 ft-lb
x₁ = 3 ft
x₂ = 18 in. = 1.5 ft
Plug the above parameters into the ratio equation:
15 : W₂ = 3² : (1.5)²
W₂ = (1.5)² . 15 / 3² = 15/4 = 3.75 ft-lb
Learn more about Hooke's Law here:
https://brainly.com/question/24086534
#SPJ4
-20 less than or equal to 4x
We will have the following:
[tex]-20\le4x[/tex]When we solve for x we will have
[tex]-\frac{20}{4}\le x\Rightarrow-5\le x[/tex]So, x is equal or grater than -5.
PLEASE HELP ME ASAP!!!
Answer:
1256
Step-by-step explanation:
A=3.14*20^2
=400*3.14
=1256
The size of a monitor is determined by the length of its diagonal. You want to buy a 19 inch monitor with a height of 11inches. What is the width of this monitor? Express your answer to the nearest tenth.XSubmINTL1217K
In this problem the diagonal of the Tv is 19 and the hight is 11 so we can use the pythagorical theorem to find the width (w) so:
[tex]19^2=11^2+w^2[/tex]and we solve for w so
[tex]\begin{gathered} w^2=19^2-11^2 \\ w=\sqrt[]{361-121} \\ w=\sqrt[]{240} \\ w=15.5 \end{gathered}[/tex]A bicyele store costs $2400 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicyeIs $120How many bicycles must the store sell each month 1o break even?Write a system of equations to represent the situation, then solve*Show both the equations and the solution
Answer:
The system of equations is:
• C(x)=2400+60x
,• R(x)=120x
The number of bicycles to break even = 40
Explanation:
Let the number of bikes sold = x
• The operating cost of the store per month = $2400
,• Cost Price Per bike = $60
Thus, the total monthly cost for the store:
[tex]C(x)=2400+60x[/tex]Next, the average selling price of each bicycle is $120, therefore, the monthly revenue of the store:
[tex]R(x)=120x[/tex]The store breaks even when the cost equals its revenue.
[tex]\begin{gathered} R(x)=C(x) \\ 120x=2400+60x \end{gathered}[/tex]We then solve for x:
[tex]\begin{gathered} \text{ Subtract 60x from both sides of the equation} \\ 120x-60x=60x-60x+2400 \\ 60x=2400 \\ \text{ Divide both sides of the equation by 60} \\ \frac{60x}{60}=\frac{2400}{60} \\ x=40 \end{gathered}[/tex]The store must sell 40 bicycles in order to break even.
Cindy struck out 7, 14, 6, 4, 5, and 6 batters in softball games this season. In discussingher stats with a newspaper reporter, Cindy's coach mentions that the average number ofCindy's strikeouts is 7. Is the coach's statement misleading? Explain why or why not.O No; the mean of her strikeouts is 7.O None of the other answers are correctO Yes, she struck out 7 batters only one time.O No; she typically strikes out 7 batters in a game.O Yes; the median of her strikeouts is 7.
Given that the batters were 7, 14,6,4,5 and 6 then to find the average, you add the batters and divide by their number
[tex]\text{sum}=7+14+6+4+5+6=42[/tex][tex]\text{Average}=\frac{42}{6}=7[/tex]Here you notice that the average is 7, so the coach's statement is true.
Your answer is , No;the mean of her strikeouts is 7
find h from this help please
The variable h, as the subject of the given formula is h = 3 / (G.V + 1)
Making a variable the subject of the formulaFrom the question, we are to make h the subject in the given formula
The given equation is
(3 - h) / V = G . h
Multiply both sides of the equation by V
V × (3 - h) / V = G . h × V
3 - h = G . h . V
Add h to both sides
3 - h + h = GhV + h
3 = GhV + h
Factorize h
3 = h(G.V + 1)
Now,
Divide both sides of the equation by (G.V + 1)
That is,
3 / (G.V + 1) = h
∴ h = 3 / (G.V + 1)
Hence, the value of h is 3 / (G.V + 1)
Learn more on Making a variable the subject of the formula here: https://brainly.com/question/20432560
#SPJ1
What is the perimeter of this rectangle?
The perimeter of the rectangle is 6.89
Perimeter of the rectangle:
The perimeter (P) of a rectangle is the total length of all the sides of the rectangle.
The formula for the perimeter of the rectangle is
P = 2(l + w)
The letter ‘P’ denotes the perimeter of a rectangle. Let l denote the length and w denote the width of the rectangle.
Given,
Here we have the graph with the following points:
(-3/2, -1 7/9), (7/2, -1 7/9), (7/2, 3 2/9), and (-3/2 3 2/9)
Now we need to find the perimeter of the rectangle.
To calculate the perimeter, first we have to find the length and width of the rectangle.
To calculate the length, we have to use the values of x axis,
That is,
=> -3/2 + 7/2
=> (-3+7)/2
=> 4/2
=> 2
Therefore, the length of the rectangle is 2.
Now, we have to find the width of the rectangle using the y axis coordinates,
=> -1 7/9 + 3 2/9
Convert the mixed fraction into normal form, then we get,
=> -16/9 + 29/9
=> (-16 + 29)/9
=> 13/9
Therefore, the width of the rectangle is 13/9
Now, we have to use this to calculate the perimeter of the triangle,
P = 2 (2 + 13/9)
P = 2 ((18+13)/9)
P = 2 (31/9)
P = 62/9
P = 6.89
Therefore, the perimeter of the rectangle is 6.89.
To know more about Perimeter of the rectangle here.
https://brainly.com/question/15287805
#SPJ1
PLEASE ASAP HELP MEEEEThe longer leg of a right triangle is 3 inches longer than the shorter leg. The hypotenuse is 6 inches longer than the shorter leg. Find the side lengths of thetriangle.Length of the shorter leg:inchesLength of the longer leg:inchesinchesLength of the hypotenuse:
In order to find the values of the sides of the triangle you take into account the relation between sides and hypotenuse.
h: hypotenuse
c1: shorter leg
c2: longer leg
Longer leg c2 is 3 inches longer than c1:
c2 = c1 + 3
hypotenuse h is 6 inches longer than c1:
h = c1 + 6
The formula for the calculation of the hypotenuse is:
h² = c1² + c2²
you replace for h and c2 in terms of c1:
(c1 + 6)² = c1² + (c1 + 3)²
You solve the previous equation for c1:
c1² + 12c1 + 36 = c1² + c1² + 6c1 + 9
c1² - 6c1 - 27 = 0
the roots of the previous equation are:
(c1 - 9 )(c1 + 3) = 0
c1 = 9
c1 = -3
You take the positive number because there is no length of sides with negative values.
Then, c2 and h are:
c2 = c1 + 3 = 9 + 3 = 12
h = c1 + 6 = 9 + 6 = 15
Hence, shorter leg is 9 inches, longer leg 12 inches and hypotenuse 15 inches
2g + (g + 5) >= 6g - 10 whats the solution set?
Answer: g ≤ 5
Step-by-step explanation: 2g + (g + 5) >= 6g - 10 ⇒ g ≤ 5
Your weekly base salary is $150. You earn $20 for each cell phone that
you sell.
a. What is the minimum amount you can earn in a week?
b. Write and solve an inequality that represents the number of cell phones
you must sell to make at least $630 a week.
c. Write and solve an inequality that represents the number of cell phones
you must sell to make at least $750 a week.
d. The company policy is that as a part-time employee, the maximum
you can earn each week is $950. Write and solve an inequality that
represents the number of cell phones you can sell each week.
The minimum that could be earned is $150. The required inequalities are solved below:
What is an inequality?
An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. There are multiple notations used to denote various types of inequalities: The symbol a b indicates that an is smaller than b. The symbol a > b indicates that an is more than b. In either scenario, a and b are not equal. These are characterized as stringent inequalities because an is either strictly less than or strictly bigger than b. Equivalence is not allowed.
(a) The minimum that could be earned is $150.
(b) The required inequality is given as 150+20x≥630
or, 20x≥630-150
or, x≥480/20
or, x≥24
(c) The required inequality is given as 150+20x≥750
or, 20x≥750-150
or, x≥600/20
or, x≥30
(d) The required inequality is given as 150+20x≤950
or, 20x≤950-150
or, x≤800/20
or, x≤40
To know more about inequalities, click on the link
https://brainly.com/question/25944814
#SPJ9
Consider the following.
sin(x) + sin(3x) = 4 sin(x) cos2(x)
Prove the identity.
Proved the identity sin(x) + sin(3x) = 4sin(x) cos²(x)
Given,
sin(x) + sin(3x) = 4 sin(x) cos²(x)
We have to prove the above given identity:
So,
sin(x) + sin(3x)
sin(x) + sin(2x + x)
By using the identity sin (A + B) we get,
sin(x) + sin (2x) cos(x) + cos (2x) sin(x)
Now use the identities:
sin 2x and cos 2x
We get,
sin(x) + 2sin(x) cos(x) cos(x) + (2cos²(x) - 1) sin(x)
Then,
sin(x) + 2sin(x) cos²(x) + 2sin(x) cos²(x) - sin(x)
We get,
4 sin(x) cos²(x)
Hence proved the identity sin(x) + sin(3x) = 4sin(x) cos²(x)
Learn more about identities here:
https://brainly.com/question/14347010
#SPJ1
suppose you sell hats for 10 dollars each and sunglasses for 5 dollars each. you know the expected number of hats sold in a day is 10 with standard deviation 1; you know the expected number of sunglasses sold in a day is 20 with standard deviation 2; you know the sale of hats and sunglasses are independent. what is the standard deviation of your revenues in a day? (round to closest dollar)
Answer:
2
Step-by-step explanation:
because average of 1 and 2 is 1.5 rounded is 2
The standard deviation of your revenues in a day is 14.
What is a standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
Let x be the revenue from hats.
And let y be the revenue from sunglasses.
And z be the total revenue.
Then according to the question:
z = 10x + 5y
You know the expected number of hats sold in a day is 10 with standard deviation 1.
σₓ = 1
σy = 2
Taking squares of both of the equation.
σₓ² = 1² = 1
σy² = 2² = 4
To find the standard deviation of your revenues in a day:
V(z) = (10)²σₓ² + 5²σy²
V(z) = (100)(1) + (25)(4)
V(z) = 200
Standard deviation,
σz² = √(200)
σz² = 10√(2)
σz² = 14.14
σz² ≈ 14
Therefore, the required standard deviation is 14.
To learn more about the standard deviation;
brainly.com/question/23907081
#SPJ2
In the figure below, XY = 15 and YZ = 17. Find XZ
The value of XZ is 32.
What is the value of XZ?
Trigonometry simply means the branch of mathematics that is concerned with functions of angles as well as their applications to calculation. It also deals with the relationship between ratios and their angles.
From the figure, XY = 15 and YZ = 17
XZ is the sum of XY and YZ:
XZ = XY + YZ
XZ = 15 + 17 = 32
Therefore, XZ is 32.
This shows the concept of trigonometry.
You can learn more about trigonometry on:
https://brainly.com/question/24438369
#SPJ1
How many times can 3x go into -14x^2
[tex]-14x^2 \div 3x\implies \cfrac{-14x^2}{3x}\implies -\cfrac{14}{3}\cdot \cfrac{x^2}{x}\implies -\cfrac{14}{3}x[/tex]
refrigerant r-410a is a mixture of refrigerants r-32 and r-125. it takes 60 pounds of r-32 and 40 pounds of r-125 to make 100 pounds of r-410a. find the ratio of r-32 to r-125. fill in the blanks with the correct answer.
The ratio of r-32 to r-125 is 3:2
A ratio in math displays how many times one number is contained in another. Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B). When both sides of a ratio are whole numbers and cannot be divided by a whole number, the ratio is in its simplest form.
Given,
Refrigerant r-32 and r-125 are the two main constituents of refrigerant r-410.
60 pounds of r-32 and 40 pounds of r-125 make up to 100 pounds of r-410.
The ratio of r-32 to r-125 = 60/40 =3/2.
Hence, the required ratio of r-32 to r-125 is 3:2
To read more about ratio, visit https://brainly.com/question/13419413
#SPJ4
Based on the given proof that the triangles are congruent
Answer:
They are congruent by SAS:
Side: AB = CB
Angle: ∠ABD = ∠CBD
Side: BD = BD
Explanation:
Two triangles are congruent if they have the same interior angles and the same length of their corresponding sides.
If two of the angles are equal, we can say that all the interior angles are equal.
So, based on the given information we get:
1. AC ⊥ BD means that AC is perpendicular to BD, therefore,
∠ADB = ∠CDB = 90°
2. It is given that ∠A = ∠C
3. Since both of their interior angles are equal, we can say that all the interior angles are equal and:
∠ABD = ∠CBD
4. The triangle ABC is isosceles because two of their interior angles are equal, therefore AB = CB
5. BD = BD because it is the same segment.
6. By SAS (Side-angle-Side) we can say that ΔABD = ΔCBD
Because the side AB is equal to side CB, the angle ABD is equal to angle CBD, and the side BD is equal to itself.
-The polynomial function p(x) = x² + 4x³ - 7x² - 22x + 24 has known factors of (x + 4) and (x - 1).
a. Rewrite p(x) as the product of linear factors.
b. Draw a rough sketch of the graph of the function.
Answer:
p(x) = (x +4)(x +3)(x -1)(x -2)see the first attachment for a graphStep-by-step explanation:
Given p(x) = x⁴ + 4x³ - 7x² - 22x + 24 with known factors (x +4) and (x -1), you want the function written as a product of linear factors, and a sketch of the graph.
A graphing calculator can help with both parts of this. It can show you the remaining zeros are -3 and 2, so the remaining linear factors are (x +3) and (x -2). At the same time, it produces a graph of the function. This is shown in the first attachment.
a. RewriteSynthetic division is a convenient way to find the remaining factors of the polynomial. Dividing by (x+4) gives ...
p(x) = (x +4)(x^3 -7x +6) . . . . . . shown in the second attachment
And dividing the cubic by (x -1) gives ...
p(x) = (x +4)(x -1)(x^2 +x -6) . . . . . . shown in the second attachment
The quadratic will have linear terms with constants that sum to 1 and have a product of -6. These constants are 3 and -2.
The rewrite of p(x) is ...
p(x) = (x +4)(x +3)(x -1)(x -2)
b. Graph
The 4th degree polynomial has a positive leading coefficient, so is above the x-axis at both the left and right ends of the graph. The graph crosses the x-axis at x = -4, -3, 1, and 2.
We note these roots are symmetrical about x=-1, so there will be a maximum at that point. That maximum is p(-1) = (-1 +4)(-1 +3)(-1 -1)(-1 -2) = 3·2·(-2)(-3) = 36. The minimum values will be found approximately halfway between -4 and -3, and again between -1 and -2. Those minima will be approximately p(-3.5) = (-.5)(.5)(-4.5)(-5.5) ≈ -6.2
The y-intercept is +24, the constant in the polynomial.
With the zero crossings, line of symmetry, local maximum, approximate local minima, and the y-intercept, we can make a passable sketch of the graph.
A graph is seen in the first attachment.